Four-Step Iteration Scheme to Approximate Fixed Point for Weak Contractions

Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems. It is known that many problems in applied sciences and engineering can be formulated as functional equations. Such equations can be transferred to fixed point theorems in an easy manner. Moreover, we use the fixed point theory to prove the existence and uniqueness of solutions of such integral and differential equations. Let X be a non-empty set. A fixed point for a self-mapping T on X is a point